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Analytical methods for calculating the buckling loads in laminated panels often assume uniform edge loads without any openings, overlooking real-world conditions with diverse non-uniform edge loads and varying cutout sizes. This study aims to explore the buckling behavior of composite panels with and without stiffeners under different non-uniform edge load distributions by developing a robust and computationally efficient finite element (FE) formulation. Buckling loads are determined for different plate aspect ratios, number of stiffeners under various non-uniform edge-loading cases. Furthermore, it addresses the effects of different layup schemes and stiffener eccentricities.The analysis employs a 9-noded heterosis plate element and a compatible 3-noded beam element, incorporating shear deformation and rotary inertia for both the plate and stiffeners. Additionally, due to the non-uniform stress distribution in the stiffened panels, a unique dynamic technique has been implemented to account for the stability performance by employing two sets of boundary conditions. The study demonstrates that maintaining stiffener eccentricity (est) within the range of 2.0 to 3.0 notably improves buckling strength depending on the type of edge loads. [ABSTRACT FROM AUTHOR]

AbstractThis present work investigates the buckling load optimization of the laminated composite plates with the elliptical hole under different non-uniform edge loads. The design objective is the maximization of the critical buckling load by determining the optimum fiber orientations in the layers. The stability equations are derived based on the first-order shear deformation theory (FSDT) of the laminated plates. The critical buckling loads are calculated using the finite element method with the nine noded rectangular element having five degrees of freedom per node. The bonobo optimizer (BO) algorithm is employed to optimize the laminated composite plates with the elliptical hole. The computer programming is developed in the MATLAB environment. Besides, the parametric studies are conducted for different types of the non-uniform edge loads, boundary conditions, cutout radius ratio and aspect ratios and the obtained numerical results are compared. Finally, the optimum results show that these factors play an imperative role in the optimum pattern and stacking sequence of the laminated composite plates with hole. The new significant findings can aid the designers in the structural design, and other industrial applications. [ABSTRACT FROM AUTHOR]

The current study presents an experimental investigation devoted to the nano‐silica and cutout effects on the axial and lateral buckling responses of carbon/epoxy fiber‐reinforced composite laminates. To this end, specimens manufactured by vacuum bagging after hand layup technique were prepared at various amounts of nano‐silica (0.5%, 1.0%, 1.5%, 2.0%, and 3.0% by weight) incorporated into epoxy resin. Furthermore, semi‐circular and circular cutouts were opened on specimens to understand cutout effect on buckling characteristics of specimens. The results demonstrated that nano‐silica had a significant effect on buckling behaviors of the carbon fiber‐reinforced composites. Regardless of cutout presences, maximum critical axial (393.33 N, 361.67 N, 320 N for W, C and S) and lateral buckling loads (34.67 N, 33 N, 32.33 N for W, C and S), were achieved from the samples having 1.5 wt. % nano‐silica. In specimens having no cutout, maximum improvements of 72.26% in axial and 48.6% in lateral directions were achieved from the specimens having 1.5 wt. % nano‐silica content. A further amount of nano‐silica addition decreased the resistance to buckling of the specimens. Also, the presence of cutouts on the specimens led to decreases in critical loads. The decreases of 1.5 wt. % nano‐silica doped specimens without cutout in the axial and lateral critical buckling loads, respectively, were seen as 22.9% and 7.24% for circular cutout, 8.75% and 5.06% for semi‐circular cutout. It was concluded that cutout processing and nano‐silica additions should be taken into consideration in a material that may be exposed the buckling failures. Highlights: Nano‐silica impact on buckling behaviors of carbon fiber‐reinforced compositesCutout effects on buckling properties of carbon fiber‐reinforced compositesFailure modes of carbon fiber‐reinforced composites with nano‐silica particlesFindings showed that 1.5 wt. % nano‐silica inclusion exhibited the best values for buckling. [ABSTRACT FROM AUTHOR]

• The elastic instability phenomenon in hyperelastic layered materials with the phases exhibiting stiffening behavior is studied • A closed-form expression for the critical stretch of macroscopic instability is derived • An analytical prediction based on Bloch-Floquet analysis for the microscopic instability is exhibited • The critical parameters and transition of instability modes are found to be highly tunable with phase stiffening This paper investigates the elastic instability behavior in soft periodic laminates subjected to finite strains, with a focus on both macroscopic and microscopic instabilities. Considering the deformation-induced phase stiffening, the Gent model with a high bulk-to-shear modulus ratio describes the behavior of incompressible phases. This non-Gaussian statistics-based model captures the non-linear constitutive results from the limited extensibility of polymeric molecular chains. This paper derives an analytical prediction for the onset of macroscopic (or longwave) instability and microscopic instability as functions of material parameters. Moreover, a numerical Bloch-Floquet analysis is imposed on identifying the instability behavior under compression. We consider a wide range of phase combinations and find that the relatively rapid stiffening of the matrix compared to the stiff layer increases the stability of laminates by decreasing the critical stretch ratio. Essentially, properly manipulating the stiffening parameters can produce an absolutely stable region without observed instability. This paper also systematically illustrates the changes in instability and the transition between macro and micro instability in fully Gent laminates, which show higher stability than fully neo-Hookean laminates with larger critical stretch ratios. The critical characteristics of instabilities, such as critical stretch ratios and critical wavenumbers, can be controlled by the choice of stiffening parameters and other material properties, enlarging the tuning of soft laminates for desired buckling patterns in practical applications. [ABSTRACT FROM AUTHOR]

This paper deals with the determination of numerical and experimental buckling loads for circular plates. In the study, plates made of isotropic material and laminated composites were taken into consideration. For the experimental part of the study, a buckling apparatus for circular plates (BACIP) was designed and manufactured to apply radial compression on plates simply supported along the outer edge, which was the most important aspect of the study. Experimental buckling loads were determined by connecting this apparatus to a tension machine. ANSYS software based on the Finite Element Method (FEM) and the analytical buckling load formula found in textbooks were also used for the determination of the numerical and analytical buckling loads. The effects of parameters such as plate thickness, number of layers, cutout sizes, and so on on critical buckling loads were investigated within the scope of the work. Comparisons of analytical, theoretical and experimental buckling loads were presented in both graphical and tabular form. The results of the experimental and theoretical buckling were found to be comparatively compatible. [ABSTRACT FROM AUTHOR]

There is an critical need in kinetic envelope design to propose sustainable solutions that can adjust to changing outdoor conditions. Bistable composite laminates are compliant systems appealing for kinetic building envelopes because they present two stable equilibrium states and transition between them with little input energy. This study characterizes the behavior of bistable laminates for kinetic screens by developing an FEA model and conducting experimental testing to validate the model and compare both data sets. The FEA model predicts the laminates' cured states, snap-through movement, and required actuation force. The FEA model can accurately predict the cured states of the laminates. Regarding the movement of the laminate and actuation force, the simulation results mostly correlate quantitatively with the experimental data and differ qualitatively. However, the FEA model can accurately predict the critical force required to snap through the laminates, which ranges between 2.5 and 4 N. [ABSTRACT FROM AUTHOR]

Double-Double (DD) laminates are discussed as an alternative to conventional laminates used in aerospace practice, which are usually composed of 0°, 45°, 90°, and −45° plies. Double-Double laminates promise advantages mainly due to simplification of design, optimization, and manufacturing processes. Stacking-sequence independent bending properties of DD laminates allow for significant simplification in context of buckling analysis, as a recent publication shows. However, not all conceivable ply-orientation combinations in DD's building block lead to it. The present short communication outlines briefly how stacking-sequence independent bending properties arise from DD's laminate architecture. The analysis reveals two valid and also a single invalid angle selection, for DD's balanced 4-ply building block. [ABSTRACT FROM AUTHOR]

This paper investigates the effect of an open hole on the stability of a compressed laminated composite plate. The study was carried out in two ways: using experimental tests and numerical analysis. As a result of the experiment, the buckling form and path of the plate were recorded. The form of buckling was determined using the ARAMIS non-contact measurement system. The critical load value was determined from the working path using the approximation method. The experimental results were verified by numerical analysis based on the finite element method. FEM investigations were carried out in terms of a linear eigenproblem analysis. This allowed the bifurcation load and the corresponding buckling form of the numerical model of the plate to be determined. Investigating the effect of the hole in the compressed plate at a critical state showed high agreement between the proposed test methods. No clear effect of the hole size on the buckling of the plate was observed. In contrast, a clear effect of the hole on the critical load value was determined. The maximum decrease in the critical load value was 14%. The same decrease was observed for the stiffness of the post-critical characteristics. It was shown that the [45|−45|90|0]s composite plate had more than three times lower strength compared to [0|−45|45|90]s and [0|90|0|90]s. The novelty of this article is the development of a research methodology based on new interdisciplinary research methods for describing the influence of the central hole on the stability of compressed composite plates. The ABAQUS system was used for the numerical analysis. [ABSTRACT FROM AUTHOR]

This study introduces multi-objective genetic algorithms for optimizing the stacking sequence of lightweight composite structures. Notably, significant emphasis is placed on adhering to engineering design guidelines specific to stacking sequence design. These guidelines are effectively integrated into the optimization problem formulation as either constraints or additional objectives. To enhance the initialization process, a novel strategy is proposed based on mechanical considerations. The method is then applied to optimize a composite laminate in terms of weight, inverse reserve factor, and buckling load factor. Three laminates were considered, and the influence of the design and the material composition on their mechanical properties were studied. This research demonstrated that a new stacking sequence [906/454/06] resulted in improved optimum designs compared to the traditional stacking sequence comprising plies at 0°, 45°, and 90° angles. These outcomes can be deemed the optimum stacking sequence, making them valuable for future applications in unmanned aerial vehicle (UAV) structures. [ABSTRACT FROM AUTHOR]

The Double-Double (DD) laminate family allows for simplification in the context of buckling analysis. Stacking-sequence discussions, known from conventional-laminate optimization, made from 0 ∘ , ± 45 ∘ , 90 ∘ plies, omit for DD. The recently presented DD-specific buckling relation is applied in this article to the 18-panel, 'horse-shoe' laminate blending reference case. The use case addresses the challenge of identifying a compatible group of laminates for differently loaded, adjacent regions, as it is a common scenario in wing covers and fuselage skins. The study demonstrates how the novel DD-laminate buckling relation simplifies the process of determining a buckling optimum for a group of laminates. The process of determining the optimum blended DD panel is presented. Its determined mass is compared with minimum masses, presented in earlier studies, which focus on stacking optimization and blending for more conventional ply orientations and laminate stacking conventions. [ABSTRACT FROM AUTHOR]

This paper presents size dependent stability analysis a cantilever micro laminated beam embedded in elastic medium by using the modified coupled stress theory which includes the length scale parameter. The micro beam subjected to compressive load is considered as three composite laminas and embedded in elastic medium which is modelled in the Winkler foundation model. In the obtaining of the governing equations, the energy principle is used. In the solution of the buckling problem, the energy based Ritz method is implemented with algebraic polynomials. In order to accuracy obtained expressions and used method, a comparative study is performed. Many parametric studies are presented in order to investigate the buckling of laminated micro beams. For this purpose, effects of stacking sequence of laminas, geometric parameters, length scale parameter, fiber orientation angle, the parameter of elastic medium on critical buckling loads of laminated micro beams are investigated. [ABSTRACT FROM AUTHOR]

Curved panels are structural elements that form the skin of wings, fuselages and tail booms in aircraft. Buckling of these structures would adversely affect aircraft performance. Due to this, the problem of buckling has been extensively researched in the past. Most of the research has been restricted to the analysis of flat composite panels and analysis of curved panels through simplifications involving geometry, material properties and boundary conditions. The present study aims to develop an analytical solution that can predict the critical buckling load for a wider range of problems. An analytical solution was developed in order to obtain the critical buckling load for a doubly-curved composite laminate under compression, shear, moment or any combination of the three loads. The assumptions of the classical laminate plate theory were used in order to obtain the displacement fields as well as strains of the laminate. The energy method was employed in order to obtain the critical buckling load for various load cases. The values obtained through the analytical solution are compared to the critical buckling loads obtained through finite element analysis (FEA). The highest deviation of critical buckling load from FEA was calculated to be 16.55%. Variation of the critical buckling load with respect to the radius of curvature, boundary conditions and stacking sequence was analyzed. The developed solution was also found to be valid for cases when radii of curvatures are unequal as well as when the length and breadth of laminate are unequal. [ABSTRACT FROM AUTHOR]

In the field of engineering materials, lightweight and ultra-lightweight composites are used in real time to a greater extent, with high-performance targeting for tailor-made systems in aerospace, automotive, and biomedical applications. Sandwich composites are among the most popular lightweight materials used in structural and vehicle-building applications. In the present investigation, one such sandwich composite laminate composed of aluminum face sheets and a high-density polyethylene core was considered to analyze sandwich composites' flexural and buckling behavior experimentally and numerically. The influence of aspect ratios, such as length to thickness and width to thickness, on the flexural and buckling performance of sandwich composite laminates was explored in the study. Laminates with different widths, namely, 10, 12, and 15 mm, and a uniform thickness and length of 3 mm and 150 mm, respectively, were used for flexural analysis, whereas laminates with widths of 10, 12, and 15 mm and a uniform thickness and length of 3 mm and 350 mm, respectively, were used for buckling analysis. The geometrical influence of the laminates on mechanical performance was studied through performance measures such as critical bending load, flexural stiffness, inter-laminar shear stress, and critical buckling load. A significant influence of aspect ratio on the mechanical behavior of the laminates was observed using both experimental and numerical approaches. Flexural behavior was observed to be better at greater widths, namely, 15 mm, and with a minimum support span of 90 mm due to reduced spring back effects and increased bending resistance. A maximum width of 15 mm allowed for a higher buckling load capacity similar to that of bending resistance. A critical buckling load of 655.8 N seemed to be the maximum and was obtained for the highest aspect ratio, b/t = 5. The soft core and ductile metal face sheets offered combined resistance to both bending and buckling. A lower aspect ratio (span to thickness) rendered these sandwich laminates better in terms of both bending and buckling. [ABSTRACT FROM AUTHOR]

A novel meshfree local method is developed in the context of Trefftz approaches to solve eigenvalue problems related to buckling and free vibration of arbitrarily shaped thin plates, potentially having complicated cutouts. The formulation is based on Kirchhoff's assumptions for thin plates with C 1 continuity of the solution function. The mesh grid is replaced by a set of nodal points containing the degrees of freedom, located over the domain and its boundaries, thus removing the need for heavy mesh generation process. A sub-domain (cloud) centered at each node and containing several adjacent nodes is considered, in which the approximation functions are defined. The bases are made from Exponential Basis Functions (EBFs), so as to automatically satisfy part of the governing PDE and thus, removing the numerical integration procedure and increasing the solution accuracy. Due to the existence of indefinite values as the critical buckling load or the free vibration frequency, Trefftz approaches have difficulties to directly apply for eigenvalue problems. To resolve this, first the homogeneous eigenvalue problem converts into a non-homogeneous problem by moving the parts with indefinite eigenvalues to the right hand side of the equality and keeping the rest on the left. The solution to the whole eigenvalue problem is approximated using a series of EBFs. Then the solution to the homogeneous part is interpolated using another series of EBFs capable of exactly satisfying the homogeneous part of the newly defined PDE, while the particular solution is approximated using the eigenvalue solution series defined at the first step. Numerical results reveal that the proposed method can efficiently produce results with high accuracy. [ABSTRACT FROM AUTHOR]

In the current study, the finite element approach has been used to investigate the effect of compression and tension types of nonlinear edge loads on the vibration and buckling performance of interlaminar hybrid fiber metal laminates (HFMLs) with and without cutouts. The effect of various hybridizations in cross ply, angle ply and quasi isotropic laminate schemes is studied extensively. Toward this a 9-noded heterosis plate element has been used to discretize the plate by taking into account the effect of shear deformation and rotary inertia. Since the stress distribution within the plate is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems. The present study consists of aluminum metal face sheets bounded with four layered hybrid laminate schemes, which includes glass and carbon layers. In which, six different hybrid configurations have been considered. The performance of each hybrid configuration along with different sized and positioned cutouts is well investigated under various nonlinear loading conditions, which are compressive and tensile in nature. [ABSTRACT FROM AUTHOR]

The cutouts are commonly found in fiber metal laminates to facilitate to pass electrical wires, water/fuel lines and sometime to facilitate easy access and inspection. Sometimes, such cutouts need to be reinforced by providing stiffener around the cutouts to avoid pre-mature failures. This article addresses the effects of reinforced cutouts and non-linearly varying edge loads on the vibration and buckling performance of inter laminar hybrid fiber metal laminates (HFMLs) by utilizing finite element approach. Toward this a 9-noded heterosis plate element has been used to discretize both plate and stiffener by taking into account the effect of shear deformation and rotary inertia. The stiffener considered in this study is spread in nature. The displacement compatibility by the plate and stiffener is maintained by using transformation matrix. The effect of eccentricity of the spread stiffener is also incorporated within the transformation matrix. Since the stress distribution within the plate is highly non-uniform in nature, the dynamic approach has been used to solve the buckling problems. The present study consists of aluminum metal face sheets bonded with four layered symmetric hybrid cross-ply laminates, in which six different hybrid configurations have been considered. The performance of each hybrid configuration along with different sized and positioned reinforced cutouts is well investigated under various nonlinear loading conditions. [ABSTRACT FROM AUTHOR]

Eccentrically stiffened plates are widely used as a structural component in many engineering applications. However, these structures are exposed to complex loading conditions, resulting in strength reduction leading to failure. This research aims to examine the stability performance of the perforated stiffened laminated composite plate subjected to non-uniform edge load under the influence of environmental conditions. Towards this, a robust and computationally efficient finite element (FE) formulation has been developed, where the plate is modeled using a 9-noded heterosis element to avoid the shear locking of the plate element and a 3-noded isoparametric beam element is adopted to model the stiffener by applying a displacement compatibility condition at the skin-stringer interface. A torsion correction factor is introduced in the beam formulation to account for the twisting of the stiffener. A unique dynamic technique is utilized to obtain the buckling load by employing two types of boundary conditions due to the non-uniform stress distribution in the perforated plate under environmental and operational loading conditions. An analysis is performed on the unstiffened plate to determine a suitable cutout shape, loading pattern and lamina scheme based on its improved stability performance. Unlike previous studies, several stiffener configurations are considered to comprehend the influence of temperature and moisture on the stability behavior of centrally placed cutout plates and obtain a stiffener configuration with improved performance. It is noticed that when the perforated stiffened plate is exposed to thermal or hygroscopic load close to a critical temperature or moisture, the buckling capacity drops suddenly in the plate attached to a stiffener of greater depth. Moreover, it is observed that when the stiffened plate is exposed to higher intensity of hygrothermal load, the plate's buckling capacity drops significantly as the thickness of the plate reduces. [ABSTRACT FROM AUTHOR]

An energy-based solution for calculating the buckling loads of partially anisotropic stiffened plates is presented, such as antisymmetric cross-ply and angle-ply laminations. A discrete approach, for the mathematical modelling and formulations of the stiffened plates, is followed. The developed formulations extend the Rayleigh–Ritz method and explore the available anisotropic unstiffened plate buckling solutions to the interesting cases of stiffened plates with some degree of material anisotropy. The examined cases consider simply supported unstiffened and stiffened plates under uniform and linearly varying compressive loading. Additionally, a reference finite element (FE) model is developed to compare the calculated buckling loads and validate the modelling approach for its accuracy. The results of the developed method are also compared with the respective experimental results for the cases where they were available in the literature. Finally, an extended discussion regarding the assumptions and restrictions of the applied Rayleigh–Ritz method is made, so that the limitations of the developed method are identified and documented. [ABSTRACT FROM AUTHOR]

The buckling enhancement of the negative Poisson's ratio (NPR) effect on a laminated plate under uniaxial compression with an in-plane translational restraint is investigated in this paper. According to the buckling equation of an orthotropic plate under biaxial compression, the critical buckling load of an NPR-laminated composite under uniaxial compression can be increased due to the induced tension force on the unloaded direction. Instead of layer angles and stacking sequence, the NPR envelope and buckling load enhancement are studied using lamination parameters in this paper. The Poisson's ratio contours are given in the feasible region of membrane lamination parameters. The results show that the negative Poisson's ratios are more sensitive to V 3 A , which represents the unbalance degree of the laminate. Furthermore, the buckling loads for various Poisson's ratio layups are investigated, and it is concluded that the buckling load increases with a decrease in Poisson's ratio for the laminated rectangular plate considering in-plane translational restraint. Finally, the inverse problem of deciding the laminate configuration to target the lamination parameters is solved using the particle swarm optimization (PSO) algorithm. [ABSTRACT FROM AUTHOR]

In this study, a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multilayered plates is developed. Analytical solution to the static and buckling responses of symmetric and anti-symmetric composite laminates is presented. The proposed theory considers secant hyperbolic function of thickness coordinate in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero shear stresses. The equilibrium equations are obtained by applying the principle of virtual work. The stiffness characteristics of cross-ply and angle-ply laminates are taken into account when solving these governing equations. The closed-form Navier solution satisfying the corresponding boundary conditions is derived for simply supported (SS) composite plates. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loading force are used to evaluate critical buckling loads. Furthermore, the impact of span thickness ratio, aspect ratios, fiber orientation, modulus ratio, etc. on static and buckling analysis plates is also studied. The validity of present formulation is demonstrated by comparing our results with some of the available results in the literature. [ABSTRACT FROM AUTHOR]

To use the laminated composite plates efficiently, it is necessary to develop appropriate analysis theories to predict accurately their structural and dynamical behavior. The analysis of the behavior of the laminated plates is an active research area because of their complex behavior. The structural instability becomes an important concern in a reliable design of composite plates. The majority of the investigations on laminated plates utilize either the classical lamination plate theory (CLPT), or the first-order shear deformation theory (FSDT). Various geometries of the plates subjected to compressive load are studied. The present work deals about a buckling analysis of simply supported symmetric composite plate with four layers. It is assumed that composite plate is surrounded by external elastic fundation. Composite plate is modeled by the finite element method and subjected to biaxial compression load. Governing equations are derived based on Classical Laminated Plate Theory (CLPT) and computed critical buckling loads were compared with numerical results. [ABSTRACT FROM AUTHOR]

The present paper aims to investigate the buckling load of functionally graded carbon-fiber-reinforced polymer (FG-CFRP) composite laminated plates under in-plane loads in a thermal environment. The effective material properties of the CFRP composite are calculated by the Mori–Tanaka homogenization method. The theoretical formulations are based on classical laminate plate theory (CLPT) and the von Kármán equations for large deflections. The governing equations are derived based on the principle of virtual work and then solved through the Navier solution. Results are obtained for the critical buckling load and temperature effect of a simply supported plate subjected to in-plane loading. A detailed numerical study is conducted to provide important insights into the effects of the functionally graded carbon fiber (CF) distribution pattern and volume fraction, total number of layers, temperature, geometrical dimension and lamination angle on the buckling load of functionally carbon-fiber-reinforced composite plates. Finally, the validation is compared with the Reddy and finite element analyses, which show consistency with each other. [ABSTRACT FROM AUTHOR]

The capabilities of the rapid tow shearing (RTS) process are explored to reduce the well-known imperfection sensitivity of axially compressed cylindrical shells. RTS deposits curvilinear carbon fibre tapes with a fibre-angle-thickness coupling that enables the in situ manufacturing of embedded rings and stringers. By blending the material's elastic modulus and wall thickness smoothly across the cylindrical surface, the load paths can be redistributed favourably with a minimal-design approach that contains part count and weight while ameliorating imperfection sensitivity. A genetic algorithm that incorporates realistic manufacturing imperfections and axial stiffness penalty is used to maximize the 99.9% reliability load of straight fibre (SF) and RTS cylinders. The axial stiffness penalty ensures that reliability does not come at the expense of stiffness. The first-order second-moment method is used to calculate statistical moments that enable an estimate of the 99.9% reliability load. Due to the fibre-angle-thickness coupling of RTS, buckling data are normalized by mass and thickness. Compared to a quasi-isotropic laminate, which corresponds to the optimal eight-layer design for a perfect cylinder, the optimized SF and RTS laminates have a 6% and 8% greater 99.9% normalized reliability load. By relaxing the axial stiffness penalty, the performance benefit can be increased such that SF and RTS cylinders exceed the 99.9% normalized reliability load of an eight-layer quasi-isotropic laminate by 23% and 37%, respectively. Both improvements (with and without penalty functions) stem largely from a reduction in the variance of the buckling-load distribution, thereby demonstrating the potential of fibre-steered cylinders in reducing the imperfection sensitivity of cylindrical shells. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'. [ABSTRACT FROM AUTHOR]

This paper examines the postbuckling behaviors of pressure-loaded laminated cylindrical shells made of carbon nanotube reinforced composite (CNTRC) under thermal environmental conditions. The shell has negative in-plane or out-of-plane effective Poisson's ratio (EPR). The thermo-mechanical properties of CNTRCs are temperature dependent. The CNT volume fraction of the shell is in a piece-wise functionally graded (FG) distribution across the shell thickness. The extended rule of mixture (EROM) model is applied to determine the thermo-mechanical properties of CNTRCs. Based on the framework of the Reddy's third order shear deformation shell theory and the von Kármán-type of kinematic assumptions, the governing partial differential equations for pressure-loaded CNTRC laminated cylindrical shells are formulated. The thermal environmental condition effect is also included. The postbuckling solution for pressure-loaded FG-CNTRC laminated cylindrical shell is obtained in the asymptotic sense by means of a singular perturbation technique in associate with a two-step perturbation approach. Numerical investigations are carried out for the (10/60/10)S shell including in-plane NPR effect, and (20/-20/20)S and (70/-70/70)S shells including out-of-plane NPR effect. Assessment is presented through numerical comparisons. [ABSTRACT FROM AUTHOR]

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Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article proposes static, free vibration, and buckling analysis of thin-walled functionally graded (FG) sandwich and composite channel-section beams. It is based on the first-order shear deformable beam theory, which can recover to classical one by ignoring the shear effect. Ritz's approximation functions are developed to solve the characteristic problems. Both results from classical and the first-order shear deformable theories are given in a unified fashion. Ritz solutions are applied for thin-walled FG sandwich channel-section beams for the first time. Numerical examples are presented in relation to many important effects such as span-to-height ratio, material parameter, lay-ups, fiber orientation and boundary conditions on the beams' deflections, natural frequencies, and critical buckling loads. New results presented in this study can be of interests to the scientific and engineering community in the future. [ABSTRACT FROM AUTHOR]

Due to the well-known geometric imperfection sensitivity, how to design a composite cylindrical shell with both adequate buckling load and lightweight characteristic is still a challenging subject. In this paper, a promising buckling design method for axially compressed composite cylindrical shells based on energy barrier approach is proposed. Reliability and advantage of this method is verified by the experimental results from numerous composite cylindrical shell specimens. Based on that, effects of laminate stacking angles on the design buckling loads are investigated in order to realize the favorable composite cylindrical shells with combined high design buckling loads and low imperfection sensitivity. [ABSTRACT FROM AUTHOR]

The aim of this study was to determine how the change of glass laminate fibres to flax fibres will affect the stability of thin-walled angle columns. Numerical analyses were conducted by the finite element method. Short L-shaped columns with different configurations of reinforcing fibres and geometric parameters were tested. The axially compressed structureswere simply supported on both ends. The lowest two bifurcation loads and their corresponding eigenmodes were determined. Several configurations of unidirectional fibre arrangement were tested. Moreover, the influence of a flange width change by ±100% and a column length change by ±33% on the bifurcation load of the compressed structure was determined. It was found that glass laminate could be successfully replaced with a bio-laminate with flax fibres. Similar results were obtained for both materials. For the same configuration of fibre arrangement, the flax laminate showed a lower sensitivity to the change in flange width than the glass material. However, the flax laminate column showed a greater sensitivity to changes in length than the glass laminate one. In a follow-up study, selected configurations will be tested experimentally. [ABSTRACT FROM AUTHOR]

This paper presents a numerical study on the stability of composite channel-section profiles weakened by cut-outs. Profiles were made from carbon fibre-reinforced polymer (CFRP) laminates and subjected to compression load. Numerical analysis carried out in the Abaqus software allowed us to determine the value of the buckling load and the corresponding buckling form. Four different laminate lay-ups were chosen to study their effects on the buckling behaviour of the profiles. Obtained results help identify the best laminate lay-up to get the highest critical buckling load for perforated columns. The performed analysis shows that [45/-45/90/0]s and [90/-45/45/0]s composite layups have the greatest impact on the buckling load. Moreover, the introduced perforation caused a change in the buckling form and a decrease in the critical load value. [ABSTRACT FROM AUTHOR]

In the present paper, buckling problems of constructions with single delamination are examined. Structures were made of unidirectional laminates and functionally graded materials (FGM). Two types of delaminations (closed and opened) were both investigated in experiments both in rectangular plates and axi-symmetric shells. The first part of the work is devoted to the formulation of contact problems (embedded, closed delaminations) with the aid of various functional inequalities. Then, computational models are discussed. To study the influence of the variable material configuration of FGMs, the fourth-order plate/shell relations were adopted. Finally, three particular problems examined are the buckling of flat rectangular plates, spherical shells, and compressed rectangular plates with elliptical delaminations. The experiments were conducted using imperfection sensitivity analysis and post-buckling non-linear analysis. The results demonstrate that the unsymmetric configurations of FGM structures lead to the reduction of buckling loads for structures with delaminations. For FG structures, those effects are described by the simple coefficient. Linear fracture mechanics were employed to distinguish the form of unilateral boundary problems (closed or opened). In the first case, the stable variations of the strain energy release rate GI with the delamination length variations were observed, whereas in the second case the unstable variations were observed. [ABSTRACT FROM AUTHOR]

This article deals with the investigation of free vibration and buckling behaviors of carbon nanotube (CNT)-reinforced cross-ply laminated composite plates. The plate kinematics is assumed to follow a first-order shear deformation theory (FSDT). After the coupled equations of motion and buckling are derived, the method of discrete singular convolution (DSC) is used for the numerical solution of the problems. Both the regularized Shannon's and Lagrange's delta kernels are used for spatial discretizing of the resulting governing equations of buckling and vibration of CNT-reinforced laminated plates. Natural frequencies and critical buckling loads are obtained for different cases. Wherever possible, the present DSC results are verified by comparing them with the existing analytical results available in the literature. Then, a detailed parametric study is performed to examine the effects of boundary conditions, CNT distributions and volume fraction, aspect ratio, length-to-width ratio, and number of layers on the frequencies and buckling loads. [ABSTRACT FROM AUTHOR]

To use the laminated composite plates efficiently, it is necessary to develop appropriate analysis theories to predict accurately their structural and dynamical behavior. The analysis of the behavior of the laminated plates is an active research area because of their complex behavior. The structural instability becomes an important concern in a reliable design of composite plates. The majority of the investigations on laminated plates utilize either the classical lamination plate theory (CLPT), or the firstorder shear deformation theory (FSDT). Various geometries of the plates subjected to compressive load are studied. The present work deals about a buckling analysis of simply supported symmetric composite plate with four layers. It is assumed that composite plate is surrounded by external elastic fundation. Composite plate is modeled by the finite element method and subjected to biaxial compression load. Governing equations are derived based on Classical Laminated Plate Theory (CLPT) and computed critical buckling loads were compared with numerical results. [ABSTRACT FROM AUTHOR]

• Using the FG-X graphene pattern in channel section struts boosts the critical buckling temperature by 12 % for clamped and 9 % for simply-supported struts, compared to the FGO pattern. • For a shape factor of b f / b w = 0.2 , changing graphene in the flanges minimally affects strut buckling temperature. However, altering the web's graphene pattern, with consistent flange reinforcement, can alter the temperature by up to 12 %. • The study on thermal pre- and post-buckling vibrations in struts with various graphene patterns reveals FGX configurations yield the highest frequencies through the pre-buckling state, though this trend shifts in the post-buckling. • Integrating an asymmetric graphene pattern (FGV) or embedding geometric imperfections sustain the primary natural frequencies of FG-GRC channel section struts above zero as they approach the critical buckling temperature. This study explores the effect of local buckling on the compressive performance of slender structural elements, particularly those with thin-walled sections. The phenomenon of local buckling significantly reduces the axial compressive stiffness, leading to a notable decrease in the load-bearing capacity of these elements. The main goal of this research is to examine how the post-buckling characteristics of polymeric composite channel section struts can be improved under thermal loading by incorporating multi-layer graphene reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To ascertain the precision and computational performance of the results derived from LW-TSDT, a three-dimensional (3D) finite element model is created in ABAQUS for comparative evaluation. An extensive analysis of nonlinear thermal instability in perfect and geometrically imperfect FG-GRC laminated channel section struts is undertaken to discern the graphene distribution patterns that are most and least effective in elevating the critical buckling temperature and natural frequencies through pre- and post-buckling conditions. The comparative analysis indicates that employing the FG-X graphene distribution pattern across the thickness of the web and flanges in channel section struts leads to a projected increase of 12 % in the critical buckling temperature for clamped channel section struts, in contrast to those that adopt the FGO graphene distribution pattern. For cases with simply-supported boundary conditions, this increase is noted to be approximately 9 %. Moreover, findings confirm that incorporating an asymmetric graphene distribution pattern (FGV) or introducing geometrical imperfections in the flanges and web that generate a bending moment within the structure from the beginning of thermal loading effectively prevents the primary natural frequencies of FG-GRC channel section struts from declining to zero close to the critical buckling temperature. This is significantly different from scenarios involving perfectly structured and symmetrically reinforced graphene distribution patterns such as FGX. [ABSTRACT FROM AUTHOR]

• A criterion for simulation of delamination is proposed. • An imperfection induced pre-buckling must be incorporated into failure analysis of open-hole laminate under in-plane compression. • Rules for selection of a scale factor for the pre-buckling analysis are set forth. • Various failures of notched laminate under compression are predicted with no parameter adjustment and no iteration. Failure prediction of open-hole laminates under compression still remains a great challenge. A number of unique mechanics theories for composites developed by the author are successfully applied to analyze in plane compression induced various failures of the notched laminates in this paper. A buckling mode must be incorporated into the analysis of the compression induced delamination, and the rules for selecting a scale factor for the buckling analysis through ABAQUS are established. To simulate delamination, the interlaminar matrix stress modification method is applied. A more pertinent criterion for delamination is proposed. When and where is delamination initiated, how can the initiated delamination be propagated and how much is the delaminated area to be attained can be easily reproduced. Intralaminar failures are estimated based on Bridging Model and the matrix true stress theory. The ultimate strength of a notched laminate is assumed when any primary layer element outside neighborhoods of the stress singularity and weak singularity points firstly attains an ultimate failure. A limited, if not the minimum, number of inputs are required all measurable independently and following existing standards with no data calibration. Except for the pre-buckling analysis, no iteration is needed for prediction of all the other failures. The predicted failure modes and ultimate compressive loads of several laminates with single or double holes agree well with our measured counterparts. [ABSTRACT FROM AUTHOR]

Thin-walled prismatic metallic members as well as structures made of laminated composite materials are routinely employed in engineering branches such as civil engineering or lightweight construction and design. Due to their thin-walled nature, such structures exhibit a number of specific characteristics that need to be taken into account during analysis and design. One of these special features is the tendency to exhibit an interaction of local, global and distortional deformation patterns which has a major impact on the structural response in the framework of first-order analysis, but also concerning the buckling, postbuckling and vibration behavior of such structures. One analysis method that takes such effects into account in a natural and straightforward way is the so-called Generalized Beam Theory (GBT), and this paper aims at providing an overview of the state of the art in this specific field. In all, 460 references are cited. • Presents a state-of-the-art survey of the Generalized Beam Theory for the analysis of thin-walled structures. • Presents an encompassing literature survey sorted by working groups around the world. • Enables researchers to find their own starting point in research in this specific field. • Includes 460 references. [ABSTRACT FROM AUTHOR]

Laminated composite shell panels take part in several engineering structures. Due to their complex nature, failure modes in composites are highly dependent on the geometry, direction of loading and orientation of the fibers. However, the design of composite parts is still a delicate task because of these fiber failure modes, which includes matrix failure modes or other so-called interlaminar interface failure such as delamination, that corresponds to the separation of adjacent layers of the laminate as a consequence of the weakening of interface layer between them. In this work, impact-induced delamination represented as a circular single delamination is investigated, as it can reduce greatly the structural integrity without getting detected. Furthermore, attention is focused on its effect upon the post-buckling response and the compressive strength of a composite panel. The delamination buckling was modelled using the cohesive element technique under Abaqus software, in order to predict delamination growth and damage propagation while observing their effects on the critical buckling load. [ABSTRACT FROM AUTHOR]

This study experimentally investigated the effects of nanoparticle reinforcement on the buckling behavior of composite materials. Different sizes of carboxylic acid functionalized multi-walled carbon nanotubes were used as nanoparticles. E-glass fiber-reinforced composite materials with polymer matrix in the [0°/90°/0°/90°]s cross-ply array with and without carbon nanotube reinforcement were produced by hand lay-up and vacuum bagging. Three types of carbon nanotubes in different sizes and proportions of 0.1%, 0.2%, 0.3%, 0.4%, and 0.5% by weight were added to the epoxy resin. For the buckling test, the samples with two clamped and two free sides were attached to the universal testing machine to apply a uniaxial compressive load. As a result of the experiments, it was found that the addition of carbon nanotube in certain proportions increases the critical buckling load of composite materials. The highest increase in the critical buckling load (26.10% increase) was achieved with a carbon nanotube reinforcement of 0.2% by weight, having an outer diameter of 10–20 nm, internal diameter of 5–10 nm, and length of 0.5–2 mm. As the carbon nanotube sizes added to the epoxy resin decreased, the buckling strength increased. [ABSTRACT FROM AUTHOR]

In this study, a new composite laminated shell model is proposed for free vibration and stability analysis based on the refined zigzag theory (RZT). In contrast to the published shell models based on the first-order shear deformation theory (FSDT), piecewise-linear zigzag functions are utilized to provide a more realistic representation of deformation states of a transverse shear-flexible shell. In the present formulation, the governing equations and boundary conditions of composite laminated shells are established by d’Alembert’s principle to obtain natural frequencies and critical buckling loadings. In order to evaluate the effectiveness and performance of the present new model for composite laminated shells, examples of free vibration and buckling analysis are carried out for cylindrical and spherical shells involving different lamination schemes and design parameters. The results are compared with the three dimensional (3D) exact, first-order and some high-order solutions in the literature. Numerical results show that the present model not only has high accuracy but also has superior computational efficiency in comparison with high-order models, such that it may show a great potential in engineering applications [ABSTRACT FROM AUTHOR]

Hybrid columns of FGM/FML type with inhomogeneous transverse structure perpendicular to their length are discussed. After that, laminated columns with different layups of laminate plies are discussed, with focus put on the effect exerted by many coupling of the stiffness submatrix on the lowest eigenvalue load. All columns were simply supported The study uses three methods for determining the lowest eigenvalues. The first two are analytical beam methods (i.e. 1D modelling approaches) based on the use of the Euler-Bernoulli theory. The proposed 1D methods are a generalisation of the well-known approach of determining the lowest eigenloads of isotropic columns. The first approach is to solve the eigenproblem directly from the differential equation of the deflection line. The second approach assumes that the curvature of the beam depends on the susceptibility of the beam. This is a fundamental assumption in the bending theory of beams and thin plates. The third method is the FEM (3D shell approach) which is used for the verification of the previous calculations. A comparison of the obtained results showed that the proposed 1D (one-dimensional) approach based on the full susceptibility matrix, which is the inverse stiffness matrix was as accurate as the 3D (three-dimensional) FEM shell model. The relative difference does not exceed 3%. Second 1D approach based on the stiffness matrix yields many times unacceptable differences relative to the reference results obtained by the FEM method. This comparison clearly demonstrates that an approach based on the assumption that curvature is directly proportional to susceptibility in flexural composite structures produces accurate results for all types of coupling. The existing literature extensively explores the impacts of stiffness matrix elements on both the linear and non-linear stability of laminate columns. However, there is a notable absence of studies focusing on the influence of susceptibility. This crucial aspect has been overlooked in prior studies. The present paper endeavors to fill this gap by shedding light on the influence of susceptibility, thereby emphasizing its significance in the analysis of laminate column stability. [ABSTRACT FROM AUTHOR]

• Higher order FEMs are proposed for bio-inspired laminated composites plates using a quasi-3D theory for the first time. • Three different FEMs are derived based on non-conforming elements with different number of nodes and degree of freedom. • No shear locking phenomenon was observed in the analyses conducted using these FEMs. • Effects of lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects. [ABSTRACT FROM AUTHOR]

The mechanics of laminates made up of elastic alternating stiff/soft layers is dominated by bending and membrane actions in the stiff layers, while transverse shear deformations concentrate in the soft interlayers producing significant zigzag warping effects. Additionally, curved geometry and large deformations can induce an interlayer thickness strain affecting the overall response of the laminate. This work presents a rotation-free Total Lagrangian large deformation curved shell model to accurately capture such a structural response. Each stiff layer is modeled as a Kirchhoff–Love shell. Without additional DOFs, each soft interlayer is modeled as a solid-shell by expressing, in finite kinematics, the displacement of top and bottom interfaces as a function of the mid-surface displacement of the upper and lower stiff layers it couples. The model is characterized by a sparse stiffness matrix compared to high-order theories and requires a small number of DOFs (3 per stiff layer) to reproduce the 3D solution. A NURBS discretization meets the high continuity of the weak form with a patch-wise reduced quadrature to avoid locking and enhance efficiency. All thickness integrals are pre-computed just once. • A nonlinear shell model is developed for stiff/soft laminates. • It is reliable for curved laminates and large deformations. • The stiff layers are isogeometric Kirchhoff–Love shells. • The soft layers are solid-shells without independent DOFs. • Warping and thickness change are captured with minimal DOFs. [ABSTRACT FROM AUTHOR]

• A novel multiscale analysis is developed to assess the buckling behavior of MWCNT-reinforced laminated composites. • Integration of microstructural factors like MWCNT clustering, alignment, and curvature in evaluating composite material performance. • Comprehensive assessment of the influence of moisture and temperature on the buckling performance of MWCNT composites. • Results successfully compared and validated with existing experimental and theoretical data. • Offers significant insights for the design and optimization of MWCNT-reinforced composites. This study introduces a detailed method for analyzing the buckling behavior of laminated composite structures strengthened with multi-walled carbon nanotubes (MWCNTs). We propose a multi-scale analysis that combines analytical and computational techniques to assess the mechanical performance of MWCNT-reinforced composites under combined moisture, temperature, and mechanical stress conditions. The Halpin-Tsai equations are used to calculate the overall stiffness properties of the nano-enhanced matrix, considering factors like MWCNT clustering, alignment, and curvature. Additionally, we incorporate the nanoscopic, size-dependent features of MWCNTs into our model. The Chamis micromechanical formulas are applied to determine the individual elastic properties of the nanocomposite layers, considering the impacts of temperature and moisture. We then explore how variables such as MWCNT content and size, along with temperature and moisture levels, influence the critical buckling load of MWCNT-based laminated composite beams and plates using our multi-scale model. Our results are successfully compared with existing experimental and theoretical data to validate our approach. The developed method offers significant insights for the design and optimization of MWCNT-reinforced composites, potentially benefiting various engineering fields, including aerospace and automotive industries. [ABSTRACT FROM AUTHOR]

The present work focused on the buckling of four-layer symmetric laminate subjected to biaxial compression. Governing equations are derived based on Classical Laminated Plate Theory (CLPT). The composite plates are bonded by an internal elastic medium and surrounded by external elastic foundation. The influences of carbon fiber orientation angle and aspect ratio on critical buckling load are demonstrated for symmetric laminate. We analyzed four lamination scheme which fiber angle orientation is equal to 0°, 30°, 45° and 90°. [ABSTRACT FROM AUTHOR]

This present study consists to analyze the mechanical buckling and the free vibration stabilities of antisymmetric cross-ply and angle-ply laminated composite plates using a refined high order shear deformation theory of four variables against five in other high order theories. Among the advantages of this new theory it takes into consideration the shearing effect in the calculation of deformation without the need for shear correction factors and giving rise to a variation of the shear stresses along the thickness and satisfying the zero shear stresses condition in faces of the plate. The laminate resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The equations of the motion are derived from Hamilton's principal. The closed form solution of simply supported rectangular plates has been obtained by using the Navier method. In addition, the effects of various parameters of the laminated composite plate on static buckling and dynamic are presented. [ABSTRACT FROM AUTHOR]

• A sequential permutation search (SPS) optimization algorithm is presented for stacking sequence design of composite plates. • SPS is a mechanics-driven algorithm utilizing convexity of lamination parameter and stiffness sensitivity. • Buckling load of composite rectangular plates with various boundaries and load conditions are optimized by SPS algorithm. • The sign optimization algorithm (SOA) is coupled in the SPS to regulate the bending-twisting coupling effects. • Comparisons are performed among SPS, LOA, and GA, demonstrating higher efficiency and robustness of SPS. Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency. [ABSTRACT FROM AUTHOR]

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